Solar protection devices are known generically, for instance, from German Utility Patent 93 15 575, in which a roof opening closable by a glass roof can be covered by means of lamellae. The lamellae are moved between two guides arranged between two guiding profiles at essentially constant separation. At the end to the rear of the vehicle, the guides have rectangular recesses extending downward at right angles to the long dimensions of the lamellae. These are storage spaces in which the lamellae can be stacked if the roof opening is left open. With the lamellae stacked, only a relatively small storage space is required for this solar protection device; thus this solar protection device is also suitable for after-market installations of sun roofs. The solar protection device need not be stored between the roof panel and the roof liner, but the lamellae pushes out of the storage space into the guides by spring pressure. The means required to apply this spring pressure are under some circumstances susceptible to damage, and are relatively expensive. For example, it can happen that the lamellae get stuck in the transition from the storage space to the guides. With this solar protection device, too, because the lamellae have to lie side by side in the closed position of the solar protection device, the solar protection device lets sufficient air through when the glass roof is raised only if the lamellae have slots for air flow.